There are 3 US Post Offices in Cleveland County serving a total of 8,176 residents equating to 2,725 residents per post office. It's estimated that approximately 13,050 packages are handled across the 3 county post offices annually. Cleveland County (formerly Dorsey County) is a county located in the U.S. state of Arkansas. Its population was 8,689 at the 2010 U.S. census. The county seat is Rison. Cleveland County is included in the Pine Bluff, AR Metropolitan Statistical Area, which is also included in the Little Rock-North Little Rock, AR Combined Statistical Area."